Assume that in the situation of Example 4.2-5, in the stationary regime, a daily number of accidents occurred to be greater than six. Find the probability that the weather on this day corresponds to the icy road condition. Comment on that it is greater then π₂.

Example 4.2-5

We include in Example 2 the information from the example of Section 3.1. Let Y₀, Y₁, Y₂ be independent Poisson r.v.’s with parameters λ₀ = 2, λ₁ = 4, λ₂ = 8, respectively. Since for large t, the probability of being in state j may be approximated by π_j, the r.v. Z_t , the number of accidents occurring on day t, may be approximated by a r.v.